Program to find the Nth term of the series 0, 14, 40, 78, 124, …

Given a number N. The task is to write a program to find the Nth term of the below series:

0, 14, 40, 78, 124 …(N Terms)

Examples:

Input: N = 4
Output: 78
For N = 4
Sum(upto 4 terms) = ( 6 * n * n - 4 * n - 2) 
                  = ( 6 * 4 * 4 - 4 * 4 - 2) 
                  =  78
Input: N = 10
Output: 557

Approach: The generalized Nth term of this series:

 nth\: Term\: of\: the\: series\: = 6*n^2-4n-2

Below is the required implementation:

C++

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// CPP program to find the N-th term of the series
// 0, 14, 40, 78, 124 ...
#include <iostream>
#include <math.h>
using namespace std;
  
// calculate sum upto Nth term of series
int nthTerm(int n)
{
    return 6 * pow(n, 2) - 4 * n - 2;
}
  
// Driver code
int main()
{
    int N = 4;
  
    cout << nthTerm(N);
  
    return 0;
}

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Java

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// Java program to find the N-th term of the series
// 0, 14, 40, 78, 124 ...
import java.util.*;
class solution
{
  
// calculate sum up to Nth term of series
static int nthTerm(int n)
{
  
    //return the final sum
    return 6 * (int)Math.pow(n, 2) - 4 * n - 2;
}
  
// Driver code
public static void main(String arr[])
{
    int N = 4;
  
    System.out.println(nthTerm(N));
  
}
}
//This code is contributed by Surendra_Gangwar

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Python3

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# Python3 program to find 
# the N-th term of the series
# 0, 14, 40, 78, 124 ...
  
# calculate sum upto Nth 
# term of series
def nthTerm(n):
    return int(6 * pow(n, 2) - 4 * n - 2)
  
# Driver code
N = 4
print(nthTerm(N))
  
# This code is contributed 
# by Shrikant13

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C#

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// C# program to find the 
// N-th term of the series
// 0, 14, 40, 78, 124 ...
using System;
  
class GFG
{
  
// calculate sum up to Nth 
// term of series
static int nthTerm(int n)
{
  
    //return the final sum
    return 6 * (int)Math.Pow(n, 2) - 
                        4 * n - 2;
}
  
// Driver code
public static void Main()
{
    int N = 4;
  
    Console.WriteLine(nthTerm(N));
}
}
  
// This code is contributed 
// by inder_verma

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PHP

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<?php
// PHP program to find the
// N-th term of the series
// 0, 14, 40, 78, 124 ...
  
// calculate sum upto 
// Nth term of series
function nthTerm($n)
{
    return 6 * pow($n, 2) - 4 * $n - 2;
}
  
// Driver code
$N = 4;
  
echo nthTerm($N);
  
// This code is contributed by 
// Akanksha Rai(Abby_akku)

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Output:

78

Time Complexity: O(1)

Note: Sum upto n terms of the above series(Sn) is:
$  S_n = 6 \sum_{i=1}^n n^2 - 4 \sum_{i=1}^n n  - 2\\ S_n=\frac{6n(n+1)(2n+1)}{6}-\frac{4n(n+1)}{2}-2n\\ S_n=n(n+1)(2n-1)-2n\\ $



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